LMFDB - Embedded newform 966.4.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$56.9958450655$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 570x^{3} - 189x^{2} + 63838x + 254320 $ x^5 - 570x^3 - 189x^2 + 63838*x + 254320
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$19.3342$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -21.3342 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -21.3342 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -42.6683 q^{10} +66.1803 q^{11} +12.0000 q^{12} -51.7853 q^{13} -14.0000 q^{14} -64.0025 q^{15} +16.0000 q^{16} -116.527 q^{17} +18.0000 q^{18} +42.0536 q^{19} -85.3367 q^{20} -21.0000 q^{21} +132.361 q^{22} -23.0000 q^{23} +24.0000 q^{24} +330.147 q^{25} -103.571 q^{26} +27.0000 q^{27} -28.0000 q^{28} +157.592 q^{29} -128.005 q^{30} +337.706 q^{31} +32.0000 q^{32} +198.541 q^{33} -233.054 q^{34} +149.339 q^{35} +36.0000 q^{36} -391.286 q^{37} +84.1071 q^{38} -155.356 q^{39} -170.673 q^{40} +230.559 q^{41} -42.0000 q^{42} +387.539 q^{43} +264.721 q^{44} -192.008 q^{45} -46.0000 q^{46} -352.569 q^{47} +48.0000 q^{48} +49.0000 q^{49} +660.294 q^{50} -349.581 q^{51} -207.141 q^{52} +567.816 q^{53} +54.0000 q^{54} -1411.90 q^{55} -56.0000 q^{56} +126.161 q^{57} +315.184 q^{58} -106.840 q^{59} -256.010 q^{60} -69.6479 q^{61} +675.411 q^{62} -63.0000 q^{63} +64.0000 q^{64} +1104.80 q^{65} +397.082 q^{66} +438.294 q^{67} -466.108 q^{68} -69.0000 q^{69} +298.678 q^{70} +634.389 q^{71} +72.0000 q^{72} +860.715 q^{73} -782.572 q^{74} +990.441 q^{75} +168.214 q^{76} -463.262 q^{77} -310.712 q^{78} +148.290 q^{79} -341.347 q^{80} +81.0000 q^{81} +461.119 q^{82} +1123.73 q^{83} -84.0000 q^{84} +2486.01 q^{85} +775.078 q^{86} +472.775 q^{87} +529.443 q^{88} -200.045 q^{89} -384.015 q^{90} +362.497 q^{91} -92.0000 q^{92} +1013.12 q^{93} -705.139 q^{94} -897.178 q^{95} +96.0000 q^{96} +457.018 q^{97} +98.0000 q^{98} +595.623 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 10 q^{5} + 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 - 10 * q^5 + 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 10 q^{5} + 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9} - 20 q^{10} + 47 q^{11} + 60 q^{12} + 74 q^{13} - 70 q^{14} - 30 q^{15} + 80 q^{16} - 4 q^{17} + 90 q^{18} + 215 q^{19} - 40 q^{20} - 105 q^{21} + 94 q^{22} - 115 q^{23} + 120 q^{24} + 535 q^{25} + 148 q^{26} + 135 q^{27} - 140 q^{28} + 273 q^{29} - 60 q^{30} + 660 q^{31} + 160 q^{32} + 141 q^{33} - 8 q^{34} + 70 q^{35} + 180 q^{36} - 71 q^{37} + 430 q^{38} + 222 q^{39} - 80 q^{40} + 428 q^{41} - 210 q^{42} + 606 q^{43} + 188 q^{44} - 90 q^{45} - 230 q^{46} + 514 q^{47} + 240 q^{48} + 245 q^{49} + 1070 q^{50} - 12 q^{51} + 296 q^{52} + 376 q^{53} + 270 q^{54} - 395 q^{55} - 280 q^{56} + 645 q^{57} + 546 q^{58} + 1062 q^{59} - 120 q^{60} + 60 q^{61} + 1320 q^{62} - 315 q^{63} + 320 q^{64} + 1755 q^{65} + 282 q^{66} + 671 q^{67} - 16 q^{68} - 345 q^{69} + 140 q^{70} + 1885 q^{71} + 360 q^{72} + 790 q^{73} - 142 q^{74} + 1605 q^{75} + 860 q^{76} - 329 q^{77} + 444 q^{78} + 738 q^{79} - 160 q^{80} + 405 q^{81} + 856 q^{82} + 774 q^{83} - 420 q^{84} + 781 q^{85} + 1212 q^{86} + 819 q^{87} + 376 q^{88} + 131 q^{89} - 180 q^{90} - 518 q^{91} - 460 q^{92} + 1980 q^{93} + 1028 q^{94} + 625 q^{95} + 480 q^{96} - 51 q^{97} + 490 q^{98} + 423 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 - 10 * q^5 + 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9 - 20 * q^10 + 47 * q^11 + 60 * q^12 + 74 * q^13 - 70 * q^14 - 30 * q^15 + 80 * q^16 - 4 * q^17 + 90 * q^18 + 215 * q^19 - 40 * q^20 - 105 * q^21 + 94 * q^22 - 115 * q^23 + 120 * q^24 + 535 * q^25 + 148 * q^26 + 135 * q^27 - 140 * q^28 + 273 * q^29 - 60 * q^30 + 660 * q^31 + 160 * q^32 + 141 * q^33 - 8 * q^34 + 70 * q^35 + 180 * q^36 - 71 * q^37 + 430 * q^38 + 222 * q^39 - 80 * q^40 + 428 * q^41 - 210 * q^42 + 606 * q^43 + 188 * q^44 - 90 * q^45 - 230 * q^46 + 514 * q^47 + 240 * q^48 + 245 * q^49 + 1070 * q^50 - 12 * q^51 + 296 * q^52 + 376 * q^53 + 270 * q^54 - 395 * q^55 - 280 * q^56 + 645 * q^57 + 546 * q^58 + 1062 * q^59 - 120 * q^60 + 60 * q^61 + 1320 * q^62 - 315 * q^63 + 320 * q^64 + 1755 * q^65 + 282 * q^66 + 671 * q^67 - 16 * q^68 - 345 * q^69 + 140 * q^70 + 1885 * q^71 + 360 * q^72 + 790 * q^73 - 142 * q^74 + 1605 * q^75 + 860 * q^76 - 329 * q^77 + 444 * q^78 + 738 * q^79 - 160 * q^80 + 405 * q^81 + 856 * q^82 + 774 * q^83 - 420 * q^84 + 781 * q^85 + 1212 * q^86 + 819 * q^87 + 376 * q^88 + 131 * q^89 - 180 * q^90 - 518 * q^91 - 460 * q^92 + 1980 * q^93 + 1028 * q^94 + 625 * q^95 + 480 * q^96 - 51 * q^97 + 490 * q^98 + 423 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	−21.3342	−1.90819	−0.954093	−	0.299510i	$-0.903177\pi$
$5$	−21.3342	−1.90819	−0.954093	+	0.299510i	$0.903177\pi$
$6$	6.00000	0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−42.6683	−1.34929
$11$	66.1803	1.81401	0.907006	−	0.421118i	$-0.138362\pi$
$11$	66.1803	1.81401	0.907006	+	0.421118i	$0.138362\pi$
$12$	12.0000	0.288675
$13$	−51.7853	−1.10482	−0.552410	−	0.833573i	$-0.686292\pi$
$13$	−51.7853	−1.10482	−0.552410	+	0.833573i	$0.686292\pi$
$14$	−14.0000	−0.267261
$15$	−64.0025	−1.10169
$16$	16.0000	0.250000
$17$	−116.527	−1.66247	−0.831233	−	0.555924i	$-0.812365\pi$
$17$	−116.527	−1.66247	−0.831233	+	0.555924i	$0.812365\pi$
$18$	18.0000	0.235702
$19$	42.0536	0.507776	0.253888	−	0.967234i	$-0.418290\pi$
$19$	42.0536	0.507776	0.253888	+	0.967234i	$0.418290\pi$
$20$	−85.3367	−0.954093
$21$	−21.0000	−0.218218
$22$	132.361	1.28270
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	24.0000	0.204124
$25$	330.147	2.64117
$26$	−103.571	−0.781226
$27$	27.0000	0.192450
$28$	−28.0000	−0.188982
$29$	157.592	1.00911	0.504553	−	0.863381i	$-0.331657\pi$
$29$	157.592	1.00911	0.504553	+	0.863381i	$0.331657\pi$
$30$	−128.005	−0.779014
$31$	337.706	1.95657	0.978286	−	0.207262i	$-0.0664552\pi$
$31$	337.706	1.95657	0.978286	+	0.207262i	$0.0664552\pi$
$32$	32.0000	0.176777
$33$	198.541	1.04732
$34$	−233.054	−1.17554
$35$	149.339	0.721227
$36$	36.0000	0.166667
$37$	−391.286	−1.73857	−0.869285	−	0.494312i	$-0.835420\pi$
$37$	−391.286	−1.73857	−0.869285	+	0.494312i	$0.835420\pi$
$38$	84.1071	0.359052
$39$	−155.356	−0.637868
$40$	−170.673	−0.674646
$41$	230.559	0.878227	0.439114	−	0.898432i	$-0.355293\pi$
$41$	230.559	0.878227	0.439114	+	0.898432i	$0.355293\pi$
$42$	−42.0000	−0.154303
$43$	387.539	1.37440	0.687199	−	0.726469i	$-0.258840\pi$
$43$	387.539	1.37440	0.687199	+	0.726469i	$0.258840\pi$
$44$	264.721	0.907006
$45$	−192.008	−0.636062
$46$	−46.0000	−0.147442
$47$	−352.569	−1.09420	−0.547101	−	0.837066i	$-0.684269\pi$
$47$	−352.569	−1.09420	−0.547101	+	0.837066i	$0.684269\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	660.294	1.86759
$51$	−349.581	−0.959826
$52$	−207.141	−0.552410
$53$	567.816	1.47161	0.735807	−	0.677191i	$-0.236803\pi$
$53$	567.816	1.47161	0.735807	+	0.677191i	$0.236803\pi$
$54$	54.0000	0.136083
$55$	−1411.90	−3.46147
$56$	−56.0000	−0.133631
$57$	126.161	0.293165
$58$	315.184	0.713545
$59$	−106.840	−0.235753	−0.117876	−	0.993028i	$-0.537609\pi$
$59$	−106.840	−0.235753	−0.117876	+	0.993028i	$0.537609\pi$
$60$	−256.010	−0.550846
$61$	−69.6479	−0.146189	−0.0730943	−	0.997325i	$-0.523287\pi$
$61$	−69.6479	−0.146189	−0.0730943	+	0.997325i	$0.523287\pi$
$62$	675.411	1.38350
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	1104.80	2.10820
$66$	397.082	0.740567
$67$	438.294	0.799196	0.399598	−	0.916691i	$-0.369150\pi$
$67$	438.294	0.799196	0.399598	+	0.916691i	$0.369150\pi$
$68$	−466.108	−0.831233
$69$	−69.0000	−0.120386
$70$	298.678	0.509984
$71$	634.389	1.06040	0.530198	−	0.847874i	$-0.322117\pi$
$71$	634.389	1.06040	0.530198	+	0.847874i	$0.322117\pi$
$72$	72.0000	0.117851
$73$	860.715	1.37999	0.689994	−	0.723815i	$-0.257613\pi$
$73$	860.715	1.37999	0.689994	+	0.723815i	$0.257613\pi$
$74$	−782.572	−1.22935
$75$	990.441	1.52488
$76$	168.214	0.253888
$77$	−463.262	−0.685632
$78$	−310.712	−0.451041
$79$	148.290	0.211189	0.105595	−	0.994409i	$-0.466325\pi$
$79$	148.290	0.211189	0.105595	+	0.994409i	$0.466325\pi$
$80$	−341.347	−0.477047
$81$	81.0000	0.111111
$82$	461.119	0.621000
$83$	1123.73	1.48608	0.743041	−	0.669245i	$-0.233382\pi$
$83$	1123.73	1.48608	0.743041	+	0.669245i	$0.233382\pi$
$84$	−84.0000	−0.109109
$85$	2486.01	3.17230
$86$	775.078	0.971846
$87$	472.775	0.582607
$88$	529.443	0.641350
$89$	−200.045	−0.238256	−0.119128	−	0.992879i	$-0.538010\pi$
$89$	−200.045	−0.238256	−0.119128	+	0.992879i	$0.538010\pi$
$90$	−384.015	−0.449764
$91$	362.497	0.417583
$92$	−92.0000	−0.104257
$93$	1013.12	1.12963
$94$	−705.139	−0.773718
$95$	−897.178	−0.968932
$96$	96.0000	0.102062
$97$	457.018	0.478383	0.239192	−	0.970972i	$-0.423118\pi$
$97$	457.018	0.478383	0.239192	+	0.970972i	$0.423118\pi$
$98$	98.0000	0.101015
$99$	595.623	0.604670
$100$	1320.59	1.32059
$101$	−31.4823	−0.0310159	−0.0155080	−	0.999880i	$-0.504937\pi$
$101$	−31.4823	−0.0310159	−0.0155080	+	0.999880i	$0.504937\pi$
$102$	−699.162	−0.678699
$103$	−921.574	−0.881605	−0.440803	−	0.897604i	$-0.645306\pi$
$103$	−921.574	−0.881605	−0.440803	+	0.897604i	$0.645306\pi$
$104$	−414.282	−0.390613
$105$	448.018	0.416400
$106$	1135.63	1.04059
$107$	−1474.93	−1.33259	−0.666293	−	0.745690i	$-0.732120\pi$
$107$	−1474.93	−1.33259	−0.666293	+	0.745690i	$0.732120\pi$
$108$	108.000	0.0962250
$109$	438.321	0.385170	0.192585	−	0.981280i	$-0.438313\pi$
$109$	438.321	0.385170	0.192585	+	0.981280i	$0.438313\pi$
$110$	−2823.81	−2.44763
$111$	−1173.86	−1.00376
$112$	−112.000	−0.0944911
$113$	431.755	0.359435	0.179717	−	0.983718i	$-0.442482\pi$
$113$	431.755	0.359435	0.179717	+	0.983718i	$0.442482\pi$
$114$	252.321	0.207299
$115$	490.686	0.397884
$116$	630.367	0.504553
$117$	−466.068	−0.368273
$118$	−213.681	−0.166702
$119$	815.689	0.628353
$120$	−512.020	−0.389507
$121$	3048.84	2.29064
$122$	−139.296	−0.103371
$123$	691.678	0.507045
$124$	1350.82	0.978286
$125$	−4376.64	−3.13167
$126$	−126.000	−0.0890871
$127$	−1190.20	−0.831601	−0.415801	−	0.909456i	$-0.636499\pi$
$127$	−1190.20	−0.831601	−0.415801	+	0.909456i	$0.636499\pi$
$128$	128.000	0.0883883
$129$	1162.62	0.793509
$130$	2209.59	1.49072
$131$	−520.947	−0.347445	−0.173723	−	0.984795i	$-0.555580\pi$
$131$	−520.947	−0.347445	−0.173723	+	0.984795i	$0.555580\pi$
$132$	794.164	0.523660
$133$	−294.375	−0.191921
$134$	876.587	0.565117
$135$	−576.023	−0.367231
$136$	−932.216	−0.587771
$137$	160.068	0.0998213	0.0499106	−	0.998754i	$-0.484106\pi$
$137$	160.068	0.0998213	0.0499106	+	0.998754i	$0.484106\pi$
$138$	−138.000	−0.0851257
$139$	2378.60	1.45144	0.725721	−	0.687989i	$-0.241506\pi$
$139$	2378.60	1.45144	0.725721	+	0.687989i	$0.241506\pi$
$140$	597.357	0.360613
$141$	−1057.71	−0.631738
$142$	1268.78	0.749814
$143$	−3427.17	−2.00416
$144$	144.000	0.0833333
$145$	−3362.09	−1.92556
$146$	1721.43	0.975799
$147$	147.000	0.0824786
$148$	−1565.14	−0.869285
$149$	−1462.55	−0.804138	−0.402069	−	0.915609i	$-0.631709\pi$
$149$	−1462.55	−0.804138	−0.402069	+	0.915609i	$0.631709\pi$
$150$	1980.88	1.07826
$151$	1430.76	0.771083	0.385541	−	0.922691i	$-0.374015\pi$
$151$	1430.76	0.771083	0.385541	+	0.922691i	$0.374015\pi$
$152$	336.429	0.179526
$153$	−1048.74	−0.554156
$154$	−926.525	−0.484815
$155$	−7204.67	−3.73350
$156$	−621.424	−0.318934
$157$	2600.16	1.32175	0.660876	−	0.750495i	$-0.270185\pi$
$157$	2600.16	1.32175	0.660876	+	0.750495i	$0.270185\pi$
$158$	296.581	0.149333
$159$	1703.45	0.849637
$160$	−682.693	−0.337323
$161$	161.000	0.0788110
$162$	162.000	0.0785674
$163$	−1854.26	−0.891024	−0.445512	−	0.895276i	$-0.646978\pi$
$163$	−1854.26	−0.891024	−0.445512	+	0.895276i	$0.646978\pi$
$164$	922.237	0.439114
$165$	−4235.71	−1.99848
$166$	2247.45	1.05082
$167$	−5.76452	−0.00267109	−0.00133554	−	0.999999i	$-0.500425\pi$
$167$	−5.76452	−0.00267109	−0.00133554	+	0.999999i	$0.500425\pi$
$168$	−168.000	−0.0771517
$169$	484.717	0.220627
$170$	4972.01	2.24315
$171$	378.482	0.169259
$172$	1550.16	0.687199
$173$	2858.05	1.25603	0.628017	−	0.778200i	$-0.283867\pi$
$173$	2858.05	1.25603	0.628017	+	0.778200i	$0.283867\pi$
$174$	945.551	0.411966
$175$	−2311.03	−0.998270
$176$	1058.89	0.453503
$177$	−320.521	−0.136112
$178$	−400.091	−0.168472
$179$	1851.76	0.773225	0.386612	−	0.922242i	$-0.373645\pi$
$179$	1851.76	0.773225	0.386612	+	0.922242i	$0.373645\pi$
$180$	−768.030	−0.318031
$181$	−1156.70	−0.475009	−0.237504	−	0.971386i	$-0.576329\pi$
$181$	−1156.70	−0.475009	−0.237504	+	0.971386i	$0.576329\pi$
$182$	724.994	0.295276
$183$	−208.944	−0.0844020
$184$	−184.000	−0.0737210
$185$	8347.77	3.31751
$186$	2026.23	0.798767
$187$	−7711.79	−3.01573
$188$	−1410.28	−0.547101
$189$	−189.000	−0.0727393
$190$	−1794.36	−0.685138
$191$	−2529.75	−0.958359	−0.479179	−	0.877717i	$-0.659066\pi$
$191$	−2529.75	−0.958359	−0.479179	+	0.877717i	$0.659066\pi$
$192$	192.000	0.0721688
$193$	−224.921	−0.0838868	−0.0419434	−	0.999120i	$-0.513355\pi$
$193$	−224.921	−0.0838868	−0.0419434	+	0.999120i	$0.513355\pi$
$194$	914.036	0.338268
$195$	3314.39	1.21717
$196$	196.000	0.0714286
$197$	−2603.10	−0.941437	−0.470719	−	0.882283i	$-0.656005\pi$
$197$	−2603.10	−0.941437	−0.470719	+	0.882283i	$0.656005\pi$
$198$	1191.25	0.427567
$199$	2882.89	1.02695	0.513474	−	0.858105i	$-0.328358\pi$
$199$	2882.89	1.02695	0.513474	+	0.858105i	$0.328358\pi$
$200$	2641.17	0.933796
$201$	1314.88	0.461416
$202$	−62.9646	−0.0219316
$203$	−1103.14	−0.381406
$204$	−1398.32	−0.479913
$205$	−4918.79	−1.67582
$206$	−1843.15	−0.623389
$207$	−207.000	−0.0695048
$208$	−828.565	−0.276205
$209$	2783.12	0.921112
$210$	896.035	0.294440
$211$	−2550.39	−0.832115	−0.416058	−	0.909338i	$-0.636589\pi$
$211$	−2550.39	−0.832115	−0.416058	+	0.909338i	$0.636589\pi$
$212$	2271.27	0.735807
$213$	1903.17	0.612220
$214$	−2949.86	−0.942281
$215$	−8267.82	−2.62261
$216$	216.000	0.0680414
$217$	−2363.94	−0.739514
$218$	876.642	0.272356
$219$	2582.15	0.796736
$220$	−5647.61	−1.73074
$221$	6034.38	1.83673
$222$	−2347.72	−0.709768
$223$	3932.61	1.18093	0.590465	−	0.807063i	$-0.298944\pi$
$223$	3932.61	1.18093	0.590465	+	0.807063i	$0.298944\pi$
$224$	−224.000	−0.0668153
$225$	2971.32	0.880392
$226$	863.510	0.254159
$227$	−3282.55	−0.959783	−0.479892	−	0.877328i	$-0.659324\pi$
$227$	−3282.55	−0.959783	−0.479892	+	0.877328i	$0.659324\pi$
$228$	504.643	0.146582
$229$	1222.04	0.352640	0.176320	−	0.984333i	$-0.443581\pi$
$229$	1222.04	0.352640	0.176320	+	0.984333i	$0.443581\pi$
$230$	981.372	0.281347
$231$	−1389.79	−0.395850
$232$	1260.73	0.356773
$233$	−566.058	−0.159157	−0.0795787	−	0.996829i	$-0.525357\pi$
$233$	−566.058	−0.159157	−0.0795787	+	0.996829i	$0.525357\pi$
$234$	−932.135	−0.260409
$235$	7521.77	2.08794
$236$	−427.361	−0.117876
$237$	444.871	0.121930
$238$	1631.38	0.444313
$239$	−4881.26	−1.32110	−0.660548	−	0.750783i	$-0.729676\pi$
$239$	−4881.26	−1.32110	−0.660548	+	0.750783i	$0.729676\pi$
$240$	−1024.04	−0.275423
$241$	−617.455	−0.165036	−0.0825182	−	0.996590i	$-0.526296\pi$
$241$	−617.455	−0.165036	−0.0825182	+	0.996590i	$0.526296\pi$
$242$	6097.68	1.61973
$243$	243.000	0.0641500
$244$	−278.592	−0.0730943
$245$	−1045.37	−0.272598
$246$	1383.36	0.358535
$247$	−2177.76	−0.561001
$248$	2701.64	0.691752
$249$	3371.18	0.857990
$250$	−8753.28	−2.21442
$251$	−786.544	−0.197794	−0.0988968	−	0.995098i	$-0.531531\pi$
$251$	−786.544	−0.197794	−0.0988968	+	0.995098i	$0.531531\pi$
$252$	−252.000	−0.0629941
$253$	−1522.15	−0.378248
$254$	−2380.40	−0.588031
$255$	7458.02	1.83153
$256$	256.000	0.0625000
$257$	−2806.32	−0.681142	−0.340571	−	0.940219i	$-0.610620\pi$
$257$	−2806.32	−0.681142	−0.340571	+	0.940219i	$0.610620\pi$
$258$	2325.23	0.561096
$259$	2739.00	0.657117
$260$	4419.19	1.05410
$261$	1418.33	0.336369
$262$	−1041.89	−0.245681
$263$	−5515.44	−1.29314	−0.646572	−	0.762853i	$-0.723798\pi$
$263$	−5515.44	−1.29314	−0.646572	+	0.762853i	$0.723798\pi$
$264$	1588.33	0.370284
$265$	−12113.9	−2.80812
$266$	−588.750	−0.135709
$267$	−600.136	−0.137557
$268$	1753.17	0.399598
$269$	−1170.46	−0.265295	−0.132648	−	0.991163i	$-0.542348\pi$
$269$	−1170.46	−0.265295	−0.132648	+	0.991163i	$0.542348\pi$
$270$	−1152.05	−0.259671
$271$	3814.37	0.855005	0.427503	−	0.904014i	$-0.359393\pi$
$271$	3814.37	0.855005	0.427503	+	0.904014i	$0.359393\pi$
$272$	−1864.43	−0.415617
$273$	1087.49	0.241091
$274$	320.136	0.0705843
$275$	21849.2	4.79112
$276$	−276.000	−0.0601929
$277$	1336.50	0.289901	0.144951	−	0.989439i	$-0.453698\pi$
$277$	1336.50	0.289901	0.144951	+	0.989439i	$0.453698\pi$
$278$	4757.20	1.02632
$279$	3039.35	0.652190
$280$	1194.71	0.254992
$281$	−6078.36	−1.29041	−0.645204	−	0.764010i	$-0.723228\pi$
$281$	−6078.36	−1.29041	−0.645204	+	0.764010i	$0.723228\pi$
$282$	−2115.42	−0.446706
$283$	1832.24	0.384859	0.192430	−	0.981311i	$-0.438363\pi$
$283$	1832.24	0.384859	0.192430	+	0.981311i	$0.438363\pi$
$284$	2537.56	0.530198
$285$	−2691.53	−0.559413
$286$	−6854.34	−1.41715
$287$	−1613.92	−0.331939
$288$	288.000	0.0589256
$289$	8665.53	1.76380
$290$	−6724.18	−1.36158
$291$	1371.05	0.276195
$292$	3442.86	0.689994
$293$	221.135	0.0440916	0.0220458	−	0.999757i	$-0.492982\pi$
$293$	221.135	0.0440916	0.0220458	+	0.999757i	$0.492982\pi$
$294$	294.000	0.0583212
$295$	2279.35	0.449860
$296$	−3130.29	−0.614677
$297$	1786.87	0.349107
$298$	−2925.09	−0.568611
$299$	1191.06	0.230371
$300$	3961.76	0.762441
$301$	−2712.77	−0.519474
$302$	2861.52	0.545238
$303$	−94.4469	−0.0179070
$304$	672.857	0.126944
$305$	1485.88	0.278955
$306$	−2097.49	−0.391847
$307$	2602.72	0.483861	0.241930	−	0.970294i	$-0.422219\pi$
$307$	2602.72	0.483861	0.241930	+	0.970294i	$0.422219\pi$
$308$	−1853.05	−0.342816
$309$	−2764.72	−0.508995
$310$	−14409.3	−2.63998
$311$	453.164	0.0826256	0.0413128	−	0.999146i	$-0.486846\pi$
$311$	453.164	0.0826256	0.0413128	+	0.999146i	$0.486846\pi$
$312$	−1242.85	−0.225520
$313$	−9153.09	−1.65292	−0.826459	−	0.562997i	$-0.809648\pi$
$313$	−9153.09	−1.65292	−0.826459	+	0.562997i	$0.809648\pi$
$314$	5200.32	0.934620
$315$	1344.05	0.240409
$316$	593.161	0.105595
$317$	7520.67	1.33250	0.666251	−	0.745728i	$-0.267898\pi$
$317$	7520.67	1.33250	0.666251	+	0.745728i	$0.267898\pi$
$318$	3406.90	0.600784
$319$	10429.5	1.83053
$320$	−1365.39	−0.238523
$321$	−4424.79	−0.769369
$322$	322.000	0.0557278
$323$	−4900.37	−0.844161
$324$	324.000	0.0555556
$325$	−17096.8	−2.91802
$326$	−3708.52	−0.630049
$327$	1314.96	0.222378
$328$	1844.47	0.310500
$329$	2467.99	0.413570
$330$	−8471.42	−1.41314
$331$	1711.57	0.284220	0.142110	−	0.989851i	$-0.454611\pi$
$331$	1711.57	0.284220	0.142110	+	0.989851i	$0.454611\pi$
$332$	4494.90	0.743041
$333$	−3521.58	−0.579523
$334$	−11.5290	−0.00188875
$335$	−9350.63	−1.52501
$336$	−336.000	−0.0545545
$337$	8005.81	1.29408	0.647039	−	0.762457i	$-0.276007\pi$
$337$	8005.81	1.29408	0.647039	+	0.762457i	$0.276007\pi$
$338$	969.435	0.156007
$339$	1295.27	0.207520
$340$	9944.02	1.58615
$341$	22349.5	3.54924
$342$	756.964	0.119684
$343$	−343.000	−0.0539949
$344$	3100.31	0.485923
$345$	1472.06	0.229719
$346$	5716.11	0.888149
$347$	−8624.62	−1.33428	−0.667138	−	0.744934i	$-0.732481\pi$
$347$	−8624.62	−1.33428	−0.667138	+	0.744934i	$0.732481\pi$
$348$	1891.10	0.291304
$349$	9205.44	1.41191	0.705954	−	0.708257i	$-0.250518\pi$
$349$	9205.44	1.41191	0.705954	+	0.708257i	$0.250518\pi$
$350$	−4622.06	−0.705884
$351$	−1398.20	−0.212623
$352$	2117.77	0.320675
$353$	−1828.88	−0.275755	−0.137877	−	0.990449i	$-0.544028\pi$
$353$	−1828.88	−0.275755	−0.137877	+	0.990449i	$0.544028\pi$
$354$	−641.042	−0.0962457
$355$	−13534.2	−2.02343
$356$	−800.181	−0.119128
$357$	2447.07	0.362780
$358$	3703.53	0.546753
$359$	−5051.05	−0.742575	−0.371287	−	0.928518i	$-0.621084\pi$
$359$	−5051.05	−0.742575	−0.371287	+	0.928518i	$0.621084\pi$
$360$	−1536.06	−0.224882
$361$	−5090.50	−0.742163
$362$	−2313.39	−0.335882
$363$	9146.51	1.32250
$364$	1449.99	0.208791
$365$	−18362.6	−2.63327
$366$	−417.888	−0.0596812
$367$	2803.10	0.398693	0.199347	−	0.979929i	$-0.436118\pi$
$367$	2803.10	0.398693	0.199347	+	0.979929i	$0.436118\pi$
$368$	−368.000	−0.0521286
$369$	2075.03	0.292742
$370$	16695.5	2.34584
$371$	−3974.71	−0.556218
$372$	4052.47	0.564813
$373$	4493.52	0.623768	0.311884	−	0.950120i	$-0.399040\pi$
$373$	4493.52	0.623768	0.311884	+	0.950120i	$0.399040\pi$
$374$	−15423.6	−2.13245
$375$	−13129.9	−1.80807
$376$	−2820.55	−0.386859
$377$	−8160.94	−1.11488
$378$	−378.000	−0.0514344
$379$	−6579.59	−0.891744	−0.445872	−	0.895097i	$-0.647106\pi$
$379$	−6579.59	−0.891744	−0.445872	+	0.895097i	$0.647106\pi$
$380$	−3588.71	−0.484466
$381$	−3570.61	−0.480125
$382$	−5059.51	−0.677662
$383$	−318.066	−0.0424345	−0.0212172	−	0.999775i	$-0.506754\pi$
$383$	−318.066	−0.0424345	−0.0212172	+	0.999775i	$0.506754\pi$
$384$	384.000	0.0510310
$385$	9883.32	1.30831
$386$	−449.842	−0.0593169
$387$	3487.85	0.458133
$388$	1828.07	0.239192
$389$	571.423	0.0744789	0.0372395	−	0.999306i	$-0.488144\pi$
$389$	571.423	0.0744789	0.0372395	+	0.999306i	$0.488144\pi$
$390$	6628.78	0.860670
$391$	2680.12	0.346648
$392$	392.000	0.0505076
$393$	−1562.84	−0.200598
$394$	−5206.20	−0.665697
$395$	−3163.65	−0.402989
$396$	2382.49	0.302335
$397$	−8885.08	−1.12325	−0.561624	−	0.827392i	$-0.689823\pi$
$397$	−8885.08	−1.12325	−0.561624	+	0.827392i	$0.689823\pi$
$398$	5765.78	0.726161
$399$	−883.125	−0.110806
$400$	5282.35	0.660294
$401$	6277.34	0.781734	0.390867	−	0.920447i	$-0.372175\pi$
$401$	6277.34	0.781734	0.390867	+	0.920447i	$0.372175\pi$
$402$	2629.76	0.326270
$403$	−17488.2	−2.16166
$404$	−125.929	−0.0155080
$405$	−1728.07	−0.212021
$406$	−2206.29	−0.269695
$407$	−25895.5	−3.15378
$408$	−2796.65	−0.339350
$409$	6329.91	0.765267	0.382633	−	0.923900i	$-0.375017\pi$
$409$	6329.91	0.765267	0.382633	+	0.923900i	$0.375017\pi$
$410$	−9837.58	−1.18498
$411$	480.203	0.0576318
$412$	−3686.29	−0.440803
$413$	747.882	0.0891062
$414$	−414.000	−0.0491473
$415$	−23973.7	−2.83572
$416$	−1657.13	−0.195306
$417$	7135.80	0.837990
$418$	5566.24	0.651325
$419$	8011.41	0.934089	0.467044	−	0.884234i	$-0.345319\pi$
$419$	8011.41	0.934089	0.467044	+	0.884234i	$0.345319\pi$
$420$	1792.07	0.208200
$421$	14772.9	1.71018	0.855090	−	0.518479i	$-0.173502\pi$
$421$	14772.9	1.71018	0.855090	+	0.518479i	$0.173502\pi$
$422$	−5100.79	−0.588394
$423$	−3173.12	−0.364734
$424$	4542.53	0.520294
$425$	−38471.0	−4.39087
$426$	3806.34	0.432905
$427$	487.535	0.0552541
$428$	−5899.72	−0.666293
$429$	−10281.5	−1.15710
$430$	−16535.6	−1.85446
$431$	−8226.95	−0.919440	−0.459720	−	0.888064i	$-0.652050\pi$
$431$	−8226.95	−0.919440	−0.459720	+	0.888064i	$0.652050\pi$
$432$	432.000	0.0481125
$433$	−3177.76	−0.352686	−0.176343	−	0.984329i	$-0.556427\pi$
$433$	−3177.76	−0.352686	−0.176343	+	0.984329i	$0.556427\pi$
$434$	−4727.88	−0.522916
$435$	−10086.3	−1.11172
$436$	1753.28	0.192585
$437$	−967.232	−0.105879
$438$	5164.29	0.563378
$439$	2162.48	0.235101	0.117550	−	0.993067i	$-0.462496\pi$
$439$	2162.48	0.235101	0.117550	+	0.993067i	$0.462496\pi$
$440$	−11295.2	−1.22381
$441$	441.000	0.0476190
$442$	12068.8	1.29876
$443$	−4620.00	−0.495492	−0.247746	−	0.968825i	$-0.579690\pi$
$443$	−4620.00	−0.495492	−0.247746	+	0.968825i	$0.579690\pi$
$444$	−4695.43	−0.501882
$445$	4267.80	0.454636
$446$	7865.23	0.835044
$447$	−4387.64	−0.464269
$448$	−448.000	−0.0472456
$449$	17289.7	1.81726	0.908630	−	0.417602i	$-0.137129\pi$
$449$	17289.7	1.81726	0.908630	+	0.417602i	$0.137129\pi$
$450$	5942.64	0.622531
$451$	15258.5	1.59311
$452$	1727.02	0.179717
$453$	4292.28	0.445185
$454$	−6565.11	−0.678669
$455$	−7733.58	−0.796826
$456$	1009.29	0.103649
$457$	7522.04	0.769948	0.384974	−	0.922927i	$-0.374210\pi$
$457$	7522.04	0.769948	0.384974	+	0.922927i	$0.374210\pi$
$458$	2444.08	0.249354
$459$	−3146.23	−0.319942
$460$	1962.74	0.198942
$461$	12837.0	1.29692	0.648458	−	0.761251i	$-0.275414\pi$
$461$	12837.0	1.29692	0.648458	+	0.761251i	$0.275414\pi$
$462$	−2779.57	−0.279908
$463$	14144.8	1.41980	0.709898	−	0.704305i	$-0.248741\pi$
$463$	14144.8	1.41980	0.709898	+	0.704305i	$0.248741\pi$
$464$	2521.47	0.252276
$465$	−21614.0	−2.15554
$466$	−1132.12	−0.112541
$467$	8146.41	0.807219	0.403609	−	0.914931i	$-0.367756\pi$
$467$	8146.41	0.807219	0.403609	+	0.914931i	$0.367756\pi$
$468$	−1864.27	−0.184137
$469$	−3068.06	−0.302068
$470$	15043.5	1.47640
$471$	7800.47	0.763114
$472$	−854.722	−0.0833512
$473$	25647.5	2.49317
$474$	889.742	0.0862177
$475$	13883.9	1.34113
$476$	3262.75	0.314177
$477$	5110.35	0.490538
$478$	−9762.51	−0.934157
$479$	−11207.6	−1.06908	−0.534541	−	0.845142i	$-0.679516\pi$
$479$	−11207.6	−1.06908	−0.534541	+	0.845142i	$0.679516\pi$
$480$	−2048.08	−0.194753
$481$	20262.9	1.92081
$482$	−1234.91	−0.116698
$483$	483.000	0.0455016
$484$	12195.4	1.14532
$485$	−9750.10	−0.912844
$486$	486.000	0.0453609
$487$	−6232.95	−0.579963	−0.289981	−	0.957032i	$-0.593649\pi$
$487$	−6232.95	−0.579963	−0.289981	+	0.957032i	$0.593649\pi$
$488$	−557.183	−0.0516855
$489$	−5562.78	−0.514433
$490$	−2090.75	−0.192756
$491$	5556.68	0.510732	0.255366	−	0.966844i	$-0.417804\pi$
$491$	5556.68	0.510732	0.255366	+	0.966844i	$0.417804\pi$
$492$	2766.71	0.253522
$493$	−18363.7	−1.67760
$494$	−4355.51	−0.396688
$495$	−12707.1	−1.15382
$496$	5403.29	0.489143
$497$	−4440.73	−0.400792
$498$	6742.35	0.606691
$499$	−7398.39	−0.663723	−0.331861	−	0.943328i	$-0.607677\pi$
$499$	−7398.39	−0.663723	−0.331861	+	0.943328i	$0.607677\pi$
$500$	−17506.6	−1.56583
$501$	−17.2936	−0.00154215
$502$	−1573.09	−0.139861
$503$	8299.64	0.735711	0.367856	−	0.929883i	$-0.380092\pi$
$503$	8299.64	0.735711	0.367856	+	0.929883i	$0.380092\pi$
$504$	−504.000	−0.0445435
$505$	671.649	0.0591841
$506$	−3044.30	−0.267461
$507$	1454.15	0.127379
$508$	−4760.81	−0.415801
$509$	1736.11	0.151182	0.0755912	−	0.997139i	$-0.475916\pi$
$509$	1736.11	0.151182	0.0755912	+	0.997139i	$0.475916\pi$
$510$	14916.0	1.29508
$511$	−6025.01	−0.521586
$512$	512.000	0.0441942
$513$	1135.45	0.0977216
$514$	−5612.64	−0.481640
$515$	19661.0	1.68227
$516$	4650.47	0.396755
$517$	−23333.2	−1.98490
$518$	5478.01	0.464652
$519$	8574.16	0.725171
$520$	8838.37	0.745362
$521$	6009.55	0.505342	0.252671	−	0.967552i	$-0.418691\pi$
$521$	6009.55	0.505342	0.252671	+	0.967552i	$0.418691\pi$
$522$	2836.65	0.237848
$523$	11942.2	0.998460	0.499230	−	0.866469i	$-0.333616\pi$
$523$	11942.2	0.998460	0.499230	+	0.866469i	$0.333616\pi$
$524$	−2083.79	−0.173723
$525$	−6933.08	−0.576352
$526$	−11030.9	−0.914391
$527$	−39351.8	−3.25273
$528$	3176.66	0.261830
$529$	529.000	0.0434783
$530$	−24227.8	−1.98564
$531$	−961.562	−0.0785843
$532$	−1177.50	−0.0959607
$533$	−11939.6	−0.970283
$534$	−1200.27	−0.0972675
$535$	31466.4	2.54282
$536$	3506.35	0.282558
$537$	5555.29	0.446422
$538$	−2340.93	−0.187592
$539$	3242.84	0.259144
$540$	−2304.09	−0.183615
$541$	9401.94	0.747174	0.373587	−	0.927595i	$-0.378128\pi$
$541$	9401.94	0.747174	0.373587	+	0.927595i	$0.378128\pi$
$542$	7628.74	0.604580
$543$	−3470.09	−0.274246
$544$	−3728.86	−0.293885
$545$	−9351.22	−0.734976
$546$	2174.98	0.170477
$547$	16210.0	1.26708	0.633539	−	0.773711i	$-0.281602\pi$
$547$	16210.0	1.26708	0.633539	+	0.773711i	$0.281602\pi$
$548$	640.271	0.0499106
$549$	−626.831	−0.0487295
$550$	43698.5	3.38783
$551$	6627.30	0.512400
$552$	−552.000	−0.0425628
$553$	−1038.03	−0.0798221
$554$	2673.01	0.204991
$555$	25043.3	1.91537
$556$	9514.41	0.725721
$557$	−8768.77	−0.667046	−0.333523	−	0.942742i	$-0.608238\pi$
$557$	−8768.77	−0.667046	−0.333523	+	0.942742i	$0.608238\pi$
$558$	6078.70	0.461168
$559$	−20068.8	−1.51846
$560$	2389.43	0.180307
$561$	−23135.4	−1.74113
$562$	−12156.7	−0.912457
$563$	8820.55	0.660287	0.330144	−	0.943931i	$-0.392903\pi$
$563$	8820.55	0.660287	0.330144	+	0.943931i	$0.392903\pi$
$564$	−4230.83	−0.315869
$565$	−9211.14	−0.685868
$566$	3664.47	0.272137
$567$	−567.000	−0.0419961
$568$	5075.12	0.374907
$569$	−3235.72	−0.238398	−0.119199	−	0.992870i	$-0.538033\pi$
$569$	−3235.72	−0.238398	−0.119199	+	0.992870i	$0.538033\pi$
$570$	−5383.07	−0.395565
$571$	−4011.90	−0.294033	−0.147016	−	0.989134i	$-0.546967\pi$
$571$	−4011.90	−0.294033	−0.147016	+	0.989134i	$0.546967\pi$
$572$	−13708.7	−1.00208
$573$	−7589.26	−0.553309
$574$	−3227.83	−0.234716
$575$	−7593.38	−0.550723
$576$	576.000	0.0416667
$577$	25158.1	1.81515	0.907577	−	0.419886i	$-0.137930\pi$
$577$	25158.1	1.81515	0.907577	+	0.419886i	$0.137930\pi$
$578$	17331.1	1.24719
$579$	−674.762	−0.0484321
$580$	−13448.4	−0.962781
$581$	−7866.08	−0.561687
$582$	2742.11	0.195299
$583$	37578.3	2.66953
$584$	6885.72	0.487899
$585$	9943.17	0.702734
$586$	442.270	0.0311775
$587$	−11792.2	−0.829157	−0.414578	−	0.910014i	$-0.636071\pi$
$587$	−11792.2	−0.829157	−0.414578	+	0.910014i	$0.636071\pi$
$588$	588.000	0.0412393
$589$	14201.7	0.993501
$590$	4558.70	0.318099
$591$	−7809.30	−0.543539
$592$	−6260.58	−0.434642
$593$	21684.6	1.50165	0.750826	−	0.660500i	$-0.229656\pi$
$593$	21684.6	1.50165	0.750826	+	0.660500i	$0.229656\pi$
$594$	3573.74	0.246856
$595$	−17402.0	−1.19902
$596$	−5850.19	−0.402069
$597$	8648.66	0.592908
$598$	2382.12	0.162897
$599$	−3505.25	−0.239100	−0.119550	−	0.992828i	$-0.538145\pi$
$599$	−3505.25	−0.239100	−0.119550	+	0.992828i	$0.538145\pi$
$600$	7923.52	0.539128
$601$	−18370.1	−1.24681	−0.623404	−	0.781900i	$-0.714251\pi$
$601$	−18370.1	−1.24681	−0.623404	+	0.781900i	$0.714251\pi$
$602$	−5425.54	−0.367323
$603$	3944.64	0.266399
$604$	5723.04	0.385541
$605$	−65044.4	−4.37096
$606$	−188.894	−0.0126622
$607$	−7894.28	−0.527873	−0.263936	−	0.964540i	$-0.585021\pi$
$607$	−7894.28	−0.527873	−0.263936	+	0.964540i	$0.585021\pi$
$608$	1345.71	0.0897630
$609$	−3309.43	−0.220205
$610$	2971.76	0.197251
$611$	18257.9	1.20890
$612$	−4194.97	−0.277078
$613$	−14892.2	−0.981224	−0.490612	−	0.871378i	$-0.663227\pi$
$613$	−14892.2	−0.981224	−0.490612	+	0.871378i	$0.663227\pi$
$614$	5205.45	0.342141
$615$	−14756.4	−0.967536
$616$	−3706.10	−0.242407
$617$	−11664.2	−0.761074	−0.380537	−	0.924766i	$-0.624261\pi$
$617$	−11664.2	−0.761074	−0.380537	+	0.924766i	$0.624261\pi$
$618$	−5529.44	−0.359914
$619$	−19243.9	−1.24956	−0.624779	−	0.780802i	$-0.714811\pi$
$619$	−19243.9	−1.24956	−0.624779	+	0.780802i	$0.714811\pi$
$620$	−28818.7	−1.86675
$621$	−621.000	−0.0401286
$622$	906.328	0.0584251
$623$	1400.32	0.0900522
$624$	−2485.69	−0.159467
$625$	52103.6	3.33463
$626$	−18306.2	−1.16879
$627$	8349.36	0.531804
$628$	10400.6	0.660876
$629$	45595.4	2.89031
$630$	2688.11	0.169995
$631$	14559.2	0.918528	0.459264	−	0.888300i	$-0.348113\pi$
$631$	14559.2	0.918528	0.459264	+	0.888300i	$0.348113\pi$
$632$	1186.32	0.0746667
$633$	−7651.18	−0.480422
$634$	15041.3	0.942221
$635$	25392.0	1.58685
$636$	6813.80	0.424819
$637$	−2537.48	−0.157831
$638$	20859.0	1.29438
$639$	5709.50	0.353466
$640$	−2730.77	−0.168661
$641$	−18468.5	−1.13800	−0.569002	−	0.822336i	$-0.692670\pi$
$641$	−18468.5	−1.13800	−0.569002	+	0.822336i	$0.692670\pi$
$642$	−8849.57	−0.544026
$643$	−7290.00	−0.447107	−0.223553	−	0.974692i	$-0.571766\pi$
$643$	−7290.00	−0.447107	−0.223553	+	0.974692i	$0.571766\pi$
$644$	644.000	0.0394055
$645$	−24803.5	−1.51416
$646$	−9800.75	−0.596912
$647$	21521.5	1.30772	0.653861	−	0.756615i	$-0.273148\pi$
$647$	21521.5	1.30772	0.653861	+	0.756615i	$0.273148\pi$
$648$	648.000	0.0392837
$649$	−7070.73	−0.427658
$650$	−34193.5	−2.06335
$651$	−7091.82	−0.426959
$652$	−7417.04	−0.445512
$653$	−9750.09	−0.584304	−0.292152	−	0.956372i	$-0.594371\pi$
$653$	−9750.09	−0.584304	−0.292152	+	0.956372i	$0.594371\pi$
$654$	2629.93	0.157245
$655$	11114.0	0.662990
$656$	3688.95	0.219557
$657$	7746.44	0.459996
$658$	4935.97	0.292438
$659$	8616.93	0.509360	0.254680	−	0.967025i	$-0.418030\pi$
$659$	8616.93	0.509360	0.254680	+	0.967025i	$0.418030\pi$
$660$	−16942.8	−0.999241
$661$	−24947.7	−1.46801	−0.734005	−	0.679144i	$-0.762351\pi$
$661$	−24947.7	−1.46801	−0.734005	+	0.679144i	$0.762351\pi$
$662$	3423.15	0.200974
$663$	18103.1	1.06043
$664$	8989.80	0.525410
$665$	6280.25	0.366222
$666$	−7043.15	−0.409785
$667$	−3624.61	−0.210413
$668$	−23.0581	−0.00133554
$669$	11797.8	0.681810
$670$	−18701.3	−1.07835
$671$	−4609.32	−0.265188
$672$	−672.000	−0.0385758
$673$	−24274.3	−1.39035	−0.695176	−	0.718840i	$-0.744673\pi$
$673$	−24274.3	−1.39035	−0.695176	+	0.718840i	$0.744673\pi$
$674$	16011.6	0.915051
$675$	8913.96	0.508294
$676$	1938.87	0.110313
$677$	−1632.55	−0.0926794	−0.0463397	−	0.998926i	$-0.514756\pi$
$677$	−1632.55	−0.0926794	−0.0463397	+	0.998926i	$0.514756\pi$
$678$	2590.53	0.146739
$679$	−3199.13	−0.180812
$680$	19888.0	1.12158
$681$	−9847.66	−0.554131
$682$	44698.9	2.50969
$683$	−20781.3	−1.16424	−0.582118	−	0.813104i	$-0.697776\pi$
$683$	−20781.3	−1.16424	−0.582118	+	0.813104i	$0.697776\pi$
$684$	1513.93	0.0846294
$685$	−3414.91	−0.190478
$686$	−686.000	−0.0381802
$687$	3666.11	0.203597
$688$	6200.62	0.343600
$689$	−29404.5	−1.62587
$690$	2944.12	0.162436
$691$	33239.9	1.82997	0.914983	−	0.403492i	$-0.132204\pi$
$691$	33239.9	1.82997	0.914983	+	0.403492i	$0.132204\pi$
$692$	11432.2	0.628017
$693$	−4169.36	−0.228544
$694$	−17249.2	−0.943476
$695$	−50745.5	−2.76962
$696$	3782.20	0.205983
$697$	−26866.4	−1.46002
$698$	18410.9	0.998370
$699$	−1698.17	−0.0918895
$700$	−9244.11	−0.499135
$701$	−1986.40	−0.107026	−0.0535130	−	0.998567i	$-0.517042\pi$
$701$	−1986.40	−0.107026	−0.0535130	+	0.998567i	$0.517042\pi$
$702$	−2796.41	−0.150347
$703$	−16455.0	−0.882804
$704$	4235.54	0.226751
$705$	22565.3	1.20547
$706$	−3657.76	−0.194988
$707$	220.376	0.0117229
$708$	−1282.08	−0.0680560
$709$	17490.9	0.926494	0.463247	−	0.886229i	$-0.346684\pi$
$709$	17490.9	0.926494	0.463247	+	0.886229i	$0.346684\pi$
$710$	−27068.3	−1.43078
$711$	1334.61	0.0703965
$712$	−1600.36	−0.0842361
$713$	−7767.23	−0.407973
$714$	4894.13	0.256524
$715$	73115.8	3.82430
$716$	7407.05	0.386612
$717$	−14643.8	−0.762736
$718$	−10102.1	−0.525080
$719$	−26786.7	−1.38940	−0.694698	−	0.719301i	$-0.744462\pi$
$719$	−26786.7	−1.38940	−0.694698	+	0.719301i	$0.744462\pi$
$720$	−3072.12	−0.159016
$721$	6451.02	0.333216
$722$	−10181.0	−0.524789
$723$	−1852.36	−0.0952838
$724$	−4626.79	−0.237504
$725$	52028.4	2.66522
$726$	18293.0	0.935149
$727$	26948.9	1.37480	0.687400	−	0.726279i	$-0.258752\pi$
$727$	26948.9	1.37480	0.687400	+	0.726279i	$0.258752\pi$
$728$	2899.98	0.147638
$729$	729.000	0.0370370
$730$	−36725.3	−1.86201
$731$	−45158.7	−2.28489
$732$	−835.775	−0.0422010
$733$	−12431.4	−0.626419	−0.313209	−	0.949684i	$-0.601404\pi$
$733$	−12431.4	−0.626419	−0.313209	+	0.949684i	$0.601404\pi$
$734$	5606.19	0.281919
$735$	−3136.12	−0.157385
$736$	−736.000	−0.0368605
$737$	29006.4	1.44975
$738$	4150.07	0.207000
$739$	−9569.99	−0.476371	−0.238185	−	0.971220i	$-0.576553\pi$
$739$	−9569.99	−0.476371	−0.238185	+	0.971220i	$0.576553\pi$
$740$	33391.1	1.65876
$741$	−6533.27	−0.323894
$742$	−7949.43	−0.393306
$743$	18238.0	0.900522	0.450261	−	0.892897i	$-0.351331\pi$
$743$	18238.0	0.900522	0.450261	+	0.892897i	$0.351331\pi$
$744$	8104.93	0.399383
$745$	31202.2	1.53444
$746$	8987.03	0.441071
$747$	10113.5	0.495361
$748$	−30847.2	−1.50787
$749$	10324.5	0.503670
$750$	−26259.8	−1.27850
$751$	14496.1	0.704355	0.352178	−	0.935933i	$-0.385441\pi$
$751$	14496.1	0.704355	0.352178	+	0.935933i	$0.385441\pi$
$752$	−5641.11	−0.273551
$753$	−2359.63	−0.114196
$754$	−16321.9	−0.788339
$755$	−30524.1	−1.47137
$756$	−756.000	−0.0363696
$757$	−35731.5	−1.71557	−0.857783	−	0.514013i	$-0.828158\pi$
$757$	−35731.5	−1.71557	−0.857783	+	0.514013i	$0.828158\pi$
$758$	−13159.2	−0.630558
$759$	−4566.44	−0.218381
$760$	−7177.43	−0.342569
$761$	−6140.55	−0.292503	−0.146251	−	0.989247i	$-0.546721\pi$
$761$	−6140.55	−0.292503	−0.146251	+	0.989247i	$0.546721\pi$
$762$	−7141.21	−0.339500
$763$	−3068.25	−0.145581
$764$	−10119.0	−0.479179
$765$	22374.1	1.05743
$766$	−636.131	−0.0300057
$767$	5532.76	0.260464
$768$	768.000	0.0360844
$769$	−26103.6	−1.22408	−0.612041	−	0.790826i	$-0.709651\pi$
$769$	−26103.6	−1.22408	−0.612041	+	0.790826i	$0.709651\pi$
$770$	19766.6	0.925117
$771$	−8418.96	−0.393257
$772$	−899.683	−0.0419434
$773$	−42582.6	−1.98136	−0.990679	−	0.136214i	$-0.956506\pi$
$773$	−42582.6	−1.98136	−0.990679	+	0.136214i	$0.956506\pi$
$774$	6975.70	0.323949
$775$	111492.	5.16765
$776$	3656.14	0.169134
$777$	8217.01	0.379387
$778$	1142.85	0.0526645
$779$	9695.84	0.445943
$780$	13257.6	0.608586
$781$	41984.1	1.92357
$782$	5360.24	0.245117
$783$	4254.98	0.194202
$784$	784.000	0.0357143
$785$	−55472.2	−2.52215
$786$	−3125.68	−0.141844
$787$	−5390.68	−0.244164	−0.122082	−	0.992520i	$-0.538957\pi$
$787$	−5390.68	−0.244164	−0.122082	+	0.992520i	$0.538957\pi$
$788$	−10412.4	−0.470719
$789$	−16546.3	−0.746597
$790$	−6327.30	−0.284956
$791$	−3022.29	−0.135854
$792$	4764.98	0.213783
$793$	3606.74	0.161512
$794$	−17770.2	−0.794257
$795$	−36341.7	−1.62127
$796$	11531.6	0.513474
$797$	21153.3	0.940136	0.470068	−	0.882630i	$-0.344229\pi$
$797$	21153.3	0.940136	0.470068	+	0.882630i	$0.344229\pi$
$798$	−1766.25	−0.0783516
$799$	41083.8	1.81908
$800$	10564.7	0.466898
$801$	−1800.41	−0.0794186
$802$	12554.7	0.552769
$803$	56962.4	2.50331
$804$	5259.52	0.230708
$805$	−3434.80	−0.150386
$806$	−34976.4	−1.52852
$807$	−3511.39	−0.153168
$808$	−251.858	−0.0109658
$809$	35880.9	1.55934	0.779670	−	0.626190i	$-0.215387\pi$
$809$	35880.9	1.55934	0.779670	+	0.626190i	$0.215387\pi$
$810$	−3456.14	−0.149921
$811$	24237.9	1.04946	0.524728	−	0.851270i	$-0.324167\pi$
$811$	24237.9	1.04946	0.524728	+	0.851270i	$0.324167\pi$
$812$	−4412.57	−0.190703
$813$	11443.1	0.493637
$814$	−51790.9	−2.23006
$815$	39559.1	1.70024
$816$	−5593.29	−0.239956
$817$	16297.4	0.697887
$818$	12659.8	0.541125
$819$	3262.47	0.139194
$820$	−19675.2	−0.837911
$821$	−30511.7	−1.29703	−0.648516	−	0.761201i	$-0.724610\pi$
$821$	−30511.7	−1.29703	−0.648516	+	0.761201i	$0.724610\pi$
$822$	960.407	0.0407519
$823$	21528.1	0.911815	0.455908	−	0.890027i	$-0.349315\pi$
$823$	21528.1	0.911815	0.455908	+	0.890027i	$0.349315\pi$
$824$	−7372.59	−0.311695
$825$	65547.7	2.76616
$826$	1495.76	0.0630076
$827$	8131.43	0.341908	0.170954	−	0.985279i	$-0.445315\pi$
$827$	8131.43	0.341908	0.170954	+	0.985279i	$0.445315\pi$
$828$	−828.000	−0.0347524
$829$	−27035.7	−1.13267	−0.566337	−	0.824174i	$-0.691640\pi$
$829$	−27035.7	−1.13267	−0.566337	+	0.824174i	$0.691640\pi$
$830$	−47947.5	−2.00516
$831$	4009.51	0.167375
$832$	−3314.26	−0.138102
$833$	−5709.82	−0.237495
$834$	14271.6	0.592548
$835$	122.981	0.00509694
$836$	11132.5	0.460556
$837$	9118.05	0.376542
$838$	16022.8	0.660500
$839$	18455.9	0.759439	0.379720	−	0.925102i	$-0.376020\pi$
$839$	18455.9	0.759439	0.379720	+	0.925102i	$0.376020\pi$
$840$	3584.14	0.147220
$841$	446.176	0.0182942
$842$	29545.7	1.20928
$843$	−18235.1	−0.745018
$844$	−10201.6	−0.416058
$845$	−10341.0	−0.420997
$846$	−6346.25	−0.257906
$847$	−21341.9	−0.865779
$848$	9085.06	0.367904
$849$	5496.71	0.222199
$850$	−76942.0	−3.10481
$851$	8999.58	0.362517
$852$	7612.67	0.306110
$853$	−21343.3	−0.856719	−0.428359	−	0.903608i	$-0.640908\pi$
$853$	−21343.3	−0.856719	−0.428359	+	0.903608i	$0.640908\pi$
$854$	975.071	0.0390705
$855$	−8074.60	−0.322977
$856$	−11799.4	−0.471140
$857$	−4738.84	−0.188887	−0.0944433	−	0.995530i	$-0.530107\pi$
$857$	−4738.84	−0.188887	−0.0944433	+	0.995530i	$0.530107\pi$
$858$	−20563.0	−0.818193
$859$	−21421.9	−0.850879	−0.425440	−	0.904987i	$-0.639881\pi$
$859$	−21421.9	−0.850879	−0.425440	+	0.904987i	$0.639881\pi$
$860$	−33071.3	−1.31130
$861$	−4841.75	−0.191645
$862$	−16453.9	−0.650142
$863$	15641.3	0.616960	0.308480	−	0.951231i	$-0.400180\pi$
$863$	15641.3	0.616960	0.308480	+	0.951231i	$0.400180\pi$
$864$	864.000	0.0340207
$865$	−60974.2	−2.39675
$866$	−6355.51	−0.249387
$867$	25996.6	1.01833
$868$	−9455.75	−0.369757
$869$	9813.90	0.383100
$870$	−20172.5	−0.786107
$871$	−22697.2	−0.882967
$872$	3506.57	0.136178
$873$	4113.16	0.159461
$874$	−1934.46	−0.0748675
$875$	30636.5	1.18366
$876$	10328.6	0.398368
$877$	40369.3	1.55436	0.777181	−	0.629277i	$-0.216649\pi$
$877$	40369.3	1.55436	0.777181	+	0.629277i	$0.216649\pi$
$878$	4324.95	0.166242
$879$	663.405	0.0254563
$880$	−22590.4	−0.865368
$881$	29081.6	1.11213	0.556063	−	0.831140i	$-0.312311\pi$
$881$	29081.6	1.11213	0.556063	+	0.831140i	$0.312311\pi$
$882$	882.000	0.0336718
$883$	−28007.6	−1.06742	−0.533709	−	0.845668i	$-0.679202\pi$
$883$	−28007.6	−1.06742	−0.533709	+	0.845668i	$0.679202\pi$
$884$	24137.5	0.918363
$885$	6838.05	0.259727
$886$	−9240.00	−0.350366
$887$	−32266.7	−1.22143	−0.610716	−	0.791850i	$-0.709118\pi$
$887$	−32266.7	−1.22143	−0.610716	+	0.791850i	$0.709118\pi$
$888$	−9390.87	−0.354884
$889$	8331.41	0.314316
$890$	8535.60	0.321476
$891$	5360.61	0.201557
$892$	15730.5	0.590465
$893$	−14826.8	−0.555610
$894$	−8775.28	−0.328288
$895$	−39505.8	−1.47546
$896$	−896.000	−0.0334077
$897$	3573.19	0.133005
$898$	34579.3	1.28500
$899$	53219.6	1.97439
$900$	11885.3	0.440196
$901$	−66165.9	−2.44651
$902$	30517.0	1.12650
$903$	−8138.32	−0.299918
$904$	3454.04	0.127079
$905$	24677.2	0.906405
$906$	8584.55	0.314793
$907$	30438.4	1.11432	0.557162	−	0.830404i	$-0.311890\pi$
$907$	30438.4	1.11432	0.557162	+	0.830404i	$0.311890\pi$
$908$	−13130.2	−0.479892
$909$	−283.341	−0.0103386
$910$	−15467.2	−0.563441
$911$	−28108.4	−1.02225	−0.511126	−	0.859506i	$-0.670772\pi$
$911$	−28108.4	−1.02225	−0.511126	+	0.859506i	$0.670772\pi$
$912$	2018.57	0.0732912
$913$	74368.5	2.69577
$914$	15044.1	0.544435
$915$	4457.64	0.161055
$916$	4888.15	0.176320
$917$	3646.63	0.131322
$918$	−6292.46	−0.226233
$919$	47605.8	1.70878	0.854391	−	0.519631i	$-0.173931\pi$
$919$	47605.8	1.70878	0.854391	+	0.519631i	$0.173931\pi$
$920$	3925.49	0.140673
$921$	7808.17	0.279357
$922$	25674.0	0.917057
$923$	−32852.0	−1.17155
$924$	−5559.15	−0.197925
$925$	−129182.	−4.59187
$926$	28289.6	1.00395
$927$	−8294.16	−0.293868
$928$	5042.94	0.178386
$929$	10253.4	0.362112	0.181056	−	0.983473i	$-0.442049\pi$
$929$	10253.4	0.362112	0.181056	+	0.983473i	$0.442049\pi$
$930$	−43228.0	−1.52420
$931$	2060.63	0.0725395
$932$	−2264.23	−0.0795787
$933$	1359.49	0.0477039
$934$	16292.8	0.570790
$935$	164525.	5.75458
$936$	−3728.54	−0.130204
$937$	24803.1	0.864761	0.432381	−	0.901691i	$-0.357674\pi$
$937$	24803.1	0.864761	0.432381	+	0.901691i	$0.357674\pi$
$938$	−6136.11	−0.213594
$939$	−27459.3	−0.954313
$940$	30087.1	1.04397
$941$	−14686.2	−0.508773	−0.254387	−	0.967103i	$-0.581874\pi$
$941$	−14686.2	−0.508773	−0.254387	+	0.967103i	$0.581874\pi$
$942$	15600.9	0.539603
$943$	−5302.86	−0.183123
$944$	−1709.44	−0.0589382
$945$	4032.16	0.138800
$946$	51294.9	1.76294
$947$	45194.1	1.55080	0.775402	−	0.631468i	$-0.217547\pi$
$947$	45194.1	1.55080	0.775402	+	0.631468i	$0.217547\pi$
$948$	1779.48	0.0609651
$949$	−44572.4	−1.52464
$950$	27767.7	0.948319
$951$	22562.0	0.769320
$952$	6525.51	0.222156
$953$	16918.9	0.575087	0.287543	−	0.957768i	$-0.407161\pi$
$953$	16918.9	0.575087	0.287543	+	0.957768i	$0.407161\pi$
$954$	10220.7	0.346863
$955$	53970.2	1.82873
$956$	−19525.0	−0.660548
$957$	31288.4	1.05686
$958$	−22415.3	−0.755955
$959$	−1120.47	−0.0377289
$960$	−4096.16	−0.137711
$961$	84254.0	2.82817
$962$	40525.8	1.35821
$963$	−13274.4	−0.444195
$964$	−2469.82	−0.0825182
$965$	4798.50	0.160072
$966$	966.000	0.0321745
$967$	32551.5	1.08251	0.541254	−	0.840859i	$-0.317950\pi$
$967$	32551.5	1.08251	0.541254	+	0.840859i	$0.317950\pi$
$968$	24390.7	0.809863
$969$	−14701.1	−0.487377
$970$	−19500.2	−0.645478
$971$	−44763.8	−1.47944	−0.739721	−	0.672914i	$-0.765043\pi$
$971$	−44763.8	−1.47944	−0.739721	+	0.672914i	$0.765043\pi$
$972$	972.000	0.0320750
$973$	−16650.2	−0.548593
$974$	−12465.9	−0.410095
$975$	−51290.3	−1.68472
$976$	−1114.37	−0.0365471
$977$	30378.2	0.994763	0.497382	−	0.867532i	$-0.334295\pi$
$977$	30378.2	0.994763	0.497382	+	0.867532i	$0.334295\pi$
$978$	−11125.6	−0.363759
$979$	−13239.1	−0.432198
$980$	−4181.50	−0.136299
$981$	3944.89	0.128390
$982$	11113.4	0.361142
$983$	23134.8	0.750646	0.375323	−	0.926894i	$-0.377532\pi$
$983$	23134.8	0.750646	0.375323	+	0.926894i	$0.377532\pi$
$984$	5533.42	0.179267
$985$	55535.0	1.79644
$986$	−36727.4	−1.18625
$987$	7403.96	0.238775
$988$	−8711.03	−0.280501
$989$	−8913.39	−0.286582
$990$	−25414.3	−0.815877
$991$	43332.4	1.38900	0.694501	−	0.719492i	$-0.255625\pi$
$991$	43332.4	1.38900	0.694501	+	0.719492i	$0.255625\pi$
$992$	10806.6	0.345876
$993$	5134.72	0.164094
$994$	−8881.45	−0.283403
$995$	−61504.0	−1.95961
$996$	13484.7	0.428995
$997$	8378.10	0.266135	0.133068	−	0.991107i	$-0.457517\pi$
$997$	8378.10	0.266135	0.133068	+	0.991107i	$0.457517\pi$
$998$	−14796.8	−0.469323
$999$	−10564.7	−0.334588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.q.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.q.1.1	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -21.3342 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -21.3342 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -42.6683 q^{10} +66.1803 q^{11} +12.0000 q^{12} -51.7853 q^{13} -14.0000 q^{14} -64.0025 q^{15} +16.0000 q^{16} -116.527 q^{17} +18.0000 q^{18} +42.0536 q^{19} -85.3367 q^{20} -21.0000 q^{21} +132.361 q^{22} -23.0000 q^{23} +24.0000 q^{24} +330.147 q^{25} -103.571 q^{26} +27.0000 q^{27} -28.0000 q^{28} +157.592 q^{29} -128.005 q^{30} +337.706 q^{31} +32.0000 q^{32} +198.541 q^{33} -233.054 q^{34} +149.339 q^{35} +36.0000 q^{36} -391.286 q^{37} +84.1071 q^{38} -155.356 q^{39} -170.673 q^{40} +230.559 q^{41} -42.0000 q^{42} +387.539 q^{43} +264.721 q^{44} -192.008 q^{45} -46.0000 q^{46} -352.569 q^{47} +48.0000 q^{48} +49.0000 q^{49} +660.294 q^{50} -349.581 q^{51} -207.141 q^{52} +567.816 q^{53} +54.0000 q^{54} -1411.90 q^{55} -56.0000 q^{56} +126.161 q^{57} +315.184 q^{58} -106.840 q^{59} -256.010 q^{60} -69.6479 q^{61} +675.411 q^{62} -63.0000 q^{63} +64.0000 q^{64} +1104.80 q^{65} +397.082 q^{66} +438.294 q^{67} -466.108 q^{68} -69.0000 q^{69} +298.678 q^{70} +634.389 q^{71} +72.0000 q^{72} +860.715 q^{73} -782.572 q^{74} +990.441 q^{75} +168.214 q^{76} -463.262 q^{77} -310.712 q^{78} +148.290 q^{79} -341.347 q^{80} +81.0000 q^{81} +461.119 q^{82} +1123.73 q^{83} -84.0000 q^{84} +2486.01 q^{85} +775.078 q^{86} +472.775 q^{87} +529.443 q^{88} -200.045 q^{89} -384.015 q^{90} +362.497 q^{91} -92.0000 q^{92} +1013.12 q^{93} -705.139 q^{94} -897.178 q^{95} +96.0000 q^{96} +457.018 q^{97} +98.0000 q^{98} +595.623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 10 q^{5} + 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 - 10 * q^5 + 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 10 q^{5} + 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9} - 20 q^{10} + 47 q^{11} + 60 q^{12} + 74 q^{13} - 70 q^{14} - 30 q^{15} + 80 q^{16} - 4 q^{17} + 90 q^{18} + 215 q^{19} - 40 q^{20} - 105 q^{21} + 94 q^{22} - 115 q^{23} + 120 q^{24} + 535 q^{25} + 148 q^{26} + 135 q^{27} - 140 q^{28} + 273 q^{29} - 60 q^{30} + 660 q^{31} + 160 q^{32} + 141 q^{33} - 8 q^{34} + 70 q^{35} + 180 q^{36} - 71 q^{37} + 430 q^{38} + 222 q^{39} - 80 q^{40} + 428 q^{41} - 210 q^{42} + 606 q^{43} + 188 q^{44} - 90 q^{45} - 230 q^{46} + 514 q^{47} + 240 q^{48} + 245 q^{49} + 1070 q^{50} - 12 q^{51} + 296 q^{52} + 376 q^{53} + 270 q^{54} - 395 q^{55} - 280 q^{56} + 645 q^{57} + 546 q^{58} + 1062 q^{59} - 120 q^{60} + 60 q^{61} + 1320 q^{62} - 315 q^{63} + 320 q^{64} + 1755 q^{65} + 282 q^{66} + 671 q^{67} - 16 q^{68} - 345 q^{69} + 140 q^{70} + 1885 q^{71} + 360 q^{72} + 790 q^{73} - 142 q^{74} + 1605 q^{75} + 860 q^{76} - 329 q^{77} + 444 q^{78} + 738 q^{79} - 160 q^{80} + 405 q^{81} + 856 q^{82} + 774 q^{83} - 420 q^{84} + 781 q^{85} + 1212 q^{86} + 819 q^{87} + 376 q^{88} + 131 q^{89} - 180 q^{90} - 518 q^{91} - 460 q^{92} + 1980 q^{93} + 1028 q^{94} + 625 q^{95} + 480 q^{96} - 51 q^{97} + 490 q^{98} + 423 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 - 10 * q^5 + 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9 - 20 * q^10 + 47 * q^11 + 60 * q^12 + 74 * q^13 - 70 * q^14 - 30 * q^15 + 80 * q^16 - 4 * q^17 + 90 * q^18 + 215 * q^19 - 40 * q^20 - 105 * q^21 + 94 * q^22 - 115 * q^23 + 120 * q^24 + 535 * q^25 + 148 * q^26 + 135 * q^27 - 140 * q^28 + 273 * q^29 - 60 * q^30 + 660 * q^31 + 160 * q^32 + 141 * q^33 - 8 * q^34 + 70 * q^35 + 180 * q^36 - 71 * q^37 + 430 * q^38 + 222 * q^39 - 80 * q^40 + 428 * q^41 - 210 * q^42 + 606 * q^43 + 188 * q^44 - 90 * q^45 - 230 * q^46 + 514 * q^47 + 240 * q^48 + 245 * q^49 + 1070 * q^50 - 12 * q^51 + 296 * q^52 + 376 * q^53 + 270 * q^54 - 395 * q^55 - 280 * q^56 + 645 * q^57 + 546 * q^58 + 1062 * q^59 - 120 * q^60 + 60 * q^61 + 1320 * q^62 - 315 * q^63 + 320 * q^64 + 1755 * q^65 + 282 * q^66 + 671 * q^67 - 16 * q^68 - 345 * q^69 + 140 * q^70 + 1885 * q^71 + 360 * q^72 + 790 * q^73 - 142 * q^74 + 1605 * q^75 + 860 * q^76 - 329 * q^77 + 444 * q^78 + 738 * q^79 - 160 * q^80 + 405 * q^81 + 856 * q^82 + 774 * q^83 - 420 * q^84 + 781 * q^85 + 1212 * q^86 + 819 * q^87 + 376 * q^88 + 131 * q^89 - 180 * q^90 - 518 * q^91 - 460 * q^92 + 1980 * q^93 + 1028 * q^94 + 625 * q^95 + 480 * q^96 - 51 * q^97 + 490 * q^98 + 423 * q^99

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